A suitable model for the potential energy surface (PES) is essential for any molecular simulation. Depending on the application of interest and the physics and chemistry at hand, different requirements such as accuracy, ability to describe relevant processes, and computational efficiency must be balanced. Machine-learning potentials have reached unprecedented trade-offs between these requirements: they can be trained to mimic density functional theory (or even better) training data with arbitrary precision, while being computationally much more efficient than electronic structure methods.
Despite their popularity and promise, machine-learning potentials have an important limitation: they are inherently short-ranged. The restriction to short ranges has two origins. First, it is common to use short real-space cutoffs to characterize the local environment of an atom. (To some extent, message-passing networks circumvent this limitation: multiple message-passing iterations take into account information from beyond the cutoff distance.) Second, the number of possible configurations of atoms within a larger cutoff sphere is enormous, making it impossible to generate relevant examples for all possibilities. Whenever long-range interactions are important, a physical model is unavoidable.
Many physically motivated models for long-range electrostatics and polarization have been developed for normal force fields and were later combined with machine-learning potentials, which handle the short-range interactions. Advantages and disadvantages of different models for long-range interactions will be discussed, and a new framework, the electron machine-learning potential (eMLP), will be presented. [1] eMLP belongs to the class of explicit electron models, [2] which approximate the electron distribution in more detail than a conventional force field with fixed charges, or even a conventional polarizable force field with atomic dipoles. Electrons or electron pairs are introduced as mobile particles with their formal charge and the freedom to polarize due to changes in geometry or the application of an external field. This is illustrated for the case of water in Figure 1. A fundamental advantage of eMLP over variable charge models, such as Qeq [3], is that all sites carry a fixed net charge, allowing the polarization of a solid to be uniquely defined. [4]
By construction, eMLP is well equipped to describe the geometry dependence of the electronic charge distribution: electron (pair) particles are located between nuclei and exhibit anistropic response due to alignment with chemical bonds. As fragments rotate or vibrate, their static and response properties naturally follow these changes in geometry. In eMLP, this enabled accurate predictions of IR activity, even for molecules on which eMLP had never been trained.
References
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- C. Bai, S. Kale, J. Herzfeld, Chem. Sci. 8 (2017) 4203–4210. https://doi.org/10.1039/C7SC01181D
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